Maybe it Did Fly, or, Maybe it Could Have Flown
Additional Information on Cornu's helicopter:~ Clicking on the linked pages will double their size. ~
- Cornu's own technical description in 'History of the Helicopter', [ Page 21, Page 22, Page 23, Page 24 ]
- Article in the 2001 Fall-Winter edition of of American Helicopter Society's publication Vertiflite.
The title is; Cornu's Helicopter ~ First in Flight? [ Page 54 & Page 54 ] by Dr. Gordon Leishman
Leishman's articles, in post #1 and above, look into the validity of Cornu's flight from the perspective of historical documentation and from the more interesting perspective of technical viability.
The Vertiflite article says
"The engineering analysis of his concepts conducted in this paper show that Cornu's claim to successful piloted flight with a helicopter is extremely dubious". On page 12 it says
".. the results in Fig.22 show that the installed power required would have need to be about 40 hp".
The craft had an unusual blade planform and it had the advantage of twin-rotors. Out of curiosity, I therefore took the specifications from Leishman's articles and from Cornu's own technical description. The data was inserted into Prouty's Momentum Theory and into his Blade Element Theory. The pitch was set at an optimal 9º and the RPM of the rotors was increased until the thrust equaled the gross weight. Surpassingly, the power required in hover by MT is 21.52 hp and by BET it is 20.98 hp.
The motor produced 24 hp, therefore, it appears that the craft was capable of flying; if the belt was not slipping.
The interesting technical question then became, why does the knowledgeable and respected Professor Leishman feel that the craft would not fly while conventional MT and BET says that it would have?
Leishman's argument to show that Cornu's helicopter could not have flown with its 24 hp engine;
1/ He uses Momentum Theory, in which he shows that the Power Required
(ideal) to hover is 14.7 hp.
2/ He then says;
"we could expect the aerodynamic efficiency of the rotors to be no more than 50% (a figure of merit or 0.5) leading to a power required of about 30 hp."
3/ He then says;
"Cornu also used an inefficient belt and pulley system to drive the rotors...." and
".... a conservative estimate of transmission losses, for Cornu to hover his machine free of the ground the installed power required would need to have been about 40 hp." This is an efficiency loss of 25%.
My counter argument to show that it could have flown;
1/ This is OK;
with reservations.
2/ Leishman's figure of merit of 0.5 is exceptionally low; for the following reasons.
a/ Cornu's rotor blade places the lift out near the tip, in the region of higher velocities.
Prouty has mentioned the advantage of reverse taper.
Sikorsky's recent patent for its X2 blade has the widest chord out nearer the tip.
b/ There is nothing, that I can find, which suggests that Cornu's blades are particularly inefficient, particularly at their low air speeds.
c/ The lack of a tail rotor should improve the FOM by up to 10%.
d/ In a discussion about Ct/sigma on this forum last year it was shown that increasing the chord and decreasing the velocity over the blade will decrease the required power. Ref.
Large Chord & Low Tip Speed This suggests that the FOM should be well above 0.5.
3/ Leishman's power loss of 25% is exceptionally high; for the following reasons.
a/ The Cornu's family business was building bicycles. Therefore, they must have been very cognizant of bearing friction and transmission losses. In fact Cornu state; "all rotating parts, including the propellers, are installed on rollers".
b/ Outside sources state that flat belts are more efficient than V-belts. In addition, the use of flat belts was well known 100 years ago, since manufacturing plants powered their machinery by flat belts from overhead line-shafts.
This suggests that the power loss should be less than 10%.
Cornu may, or may not, have flown, however it appears to me that he could have.
Does anyone wish to expand on the pros and cons regarding the viability of flight?
Dave